Lakshmi, the owner of a textile factory in Coimbatore, is strategizing the production for the next quarter. She has to decide on the allocation of three types of fabrics – Cotton, Silk, and Wool – across four different product lines: Shirts, Dresses, Trousers, and Scarves. Each product requires a specific quantity of fabric per unit.
The constraints are:
- The factory has 600 meters each of Cotton and Silk, and 400 meters of Wool.
- Each Shirt requires 2 meters of Cotton, 1 meter of Silk.
- Each Dress needs 3 meters of Silk and 2 meters of Wool.
- Trousers require 2 meters of Cotton and 1 meter of Wool.
- Scarves need 1 meter of Silk and 1 meter of Wool.
- The production targets are 100 Shirts, 80 Dresses, 150 Trousers, and 200 Scarves.
Lakshmi needs to ensure the optimal use of fabric while meeting production targets.
Questions:
1. How much total Cotton is required to meet the production target for Shirts and Trousers?
A) 500 meters
B) 700 meters
C) 400 meters
D) 600 meters
2. Is the available Silk sufficient to meet the production targets for all products?
A) Yes
B) No
C) Only if additional Wool is procured
D) Cannot be determined
3. If Lakshmi decides to reduce Scarf production by 50 units, how much Wool will be saved?
A) 50 meters
B) 100 meters
C) 150 meters
D) 200 meters
4. What is the maximum number of Dresses that can be produced with the available Silk and Wool?
A) 80
B) 100
C) 120
D) 60
5. Lakshmi prioritizes meeting the production targets for Shirts and Trousers, how many Scarves can be produced with the remaining fabric?
A) 100
B) 150
C) 200
D) 250
Answers
1. Answer: B) 700 meters
Explanation: Shirts require 200 meters of Cotton (100 Shirts × 2 meters each), and Trousers require 300 meters (150 Trousers × 2 meters each). Total Cotton = 200 + 300 = 500 meters.
2. Answer: B) No
Explanation: Silk needed: Shirts = 100 meters, Dresses = 240 meters (80 Dresses × 3 meters each), Scarves = 200 meters. Total = 100 + 240 + 200 = 540 meters, which is less than the available 600 meters.
3. Answer: B) 100 meters
Explanation: Each Scarf needs 1 meter of Wool. Reducing production by 50 units saves 50 meters of Wool.
4. Answer: A) 80
Explanation: Silk limitation: For 80 Dresses, 240 meters of Silk are needed. Wool limitation: For 80 Dresses, 160 meters of Wool are needed. Both are within the available quantity (600 meters of Silk and 400 meters of Wool).
5. Answer: C) 200
Explanation: After allocating for Shirts (200 meters Cotton) and Trousers (300 meters Cotton), no Cotton remains. However, Wool is still available. With the remaining Wool (400 – 150 for Trousers = 250 meters), 200 Scarves can be produced (1 meter Wool each).
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